Commit graph

2061 commits

Author SHA1 Message Date
Leonardo de Moura
29e448f034 fix(library/simplifier): remove support in the simplifier for (forall x : A, B x) when it is not a proposition, the problem is that hpiext axiom produces an equality in a too big universe
For example, in the hpiext axiom, the resultant equality if for (Type M+1)

axiom hpiext {A A' : TypeM} {B : A -> TypeM} {B' : A' -> TypeM} :
      A = A' -> (∀ x x', x == x' -> B x = B' x') -> (∀ x, B x) = (∀ x, B' x)

even if the actual arguments A, A’, B, B’ "live" in a much smaller universe (e.g., Type).

So, it would be great if we could move the resultant equality back to the right universe.
I don't see how to do it right now.

The other solution would require a major rewrite of the code base.
We would have to support universe level arguments like Agda, and write the axiom hpiext as:

axiom hpiext {l : level} {A A' : (Type l)} {B : A -> (Type l)} {B' : A' -> (Type l)} :
      A = A' -> (∀ x x', x == x' -> B x = B' x') -> (∀ x, B x) = (∀ x, B' x)

This is the first instance I found where it is really handy to have this feature.
I think this would be a super clean solution, but it would require a big rewrite in the code base.
Another problem is that the actual semantics that Agda has for this kind of construction is not clear to me.
For instance, sometimes Agda reports that the type of an expression is (Set omega).

An easier to implement hack is to support "axiom templates".
We create instances of hipext "on-demand" for different universe levels.
This is essentially what Coq does, since the universe levels are implicit in Coq.
This is not as clean as the Agda approach, but it is much easier to implement.

A super dirty trick is to include some instances of hpiext for commonly used universes
(e.g., Type and (Type 1)).

Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2014-01-26 12:10:34 -08:00
Leonardo de Moura
52ee9b35dd feat(library/simplifier): add support for simplifying even when heq module is not available
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2014-01-26 11:29:36 -08:00
Leonardo de Moura
fafaa7e78e fix(library/simplifier): remove hack for handling some constants that expect an argument of type TypeU, the new approach is general
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2014-01-26 10:10:57 -08:00
Leonardo de Moura
89bb5fbf19 chore(library/simplifier): fix style
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2014-01-26 00:36:17 -08:00
Leonardo de Moura
844572c382 feat(library/simplifier): support for dependent simplification in Pi/forall expressions
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2014-01-26 00:32:05 -08:00
Leonardo de Moura
e8bba1ebf3 fix(frontends/lean/frontend): the definition of the explicit version @f must be definitionally equal to f
Before this commit, the explicit version @f of a constant f with implicit arguments as not definitionally equal to f.

For example, if we had

variable f {A : Type} : A -> Bool

Then, the definition of @f was

definition @f (A : Type) (a : A) : Bool := f A a

This definition is equivalent to
     fun A a, f A a
which is not definitionally equal to
     f
since definitionally equality in Lean ignores Eta conversion.

Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2014-01-25 20:34:28 -08:00
Leonardo de Moura
6bc1537e25 feat(frontends/lean/parser): allow the user to write (Type) without providing a level
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2014-01-25 20:17:36 -08:00
Leonardo de Moura
9fb3ccb4c0 feat(library/simplifier): support for dependent simplification in lambda expressions
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2014-01-25 16:54:42 -08:00
Leonardo de Moura
5b13ef1b90 test(tests/lean): new simplifier test
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2014-01-25 10:56:49 -08:00
Leonardo de Moura
7015089734 fix(library/simplifier): move to locally nameless approach in the simplifier. Contextual simplification may add rewriting rules with free variables, and it is a mess to manage them when using de Bruijn indices
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2014-01-25 10:49:44 -08:00
Leonardo de Moura
df3129e80d fix(library/hop_match): typo
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2014-01-25 10:08:53 -08:00
Leonardo de Moura
7a4eb4b8ed feat(library/simplifier): contextual simplification for A -> B
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2014-01-24 22:32:55 -08:00
Leonardo de Moura
c2381e43f1 fix(library/simplifier): bug in cast elimination
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2014-01-24 21:25:09 -08:00
Leonardo de Moura
2bb33c55fe feat(builtin/kernel): add more theorems useful for simplification
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2014-01-24 18:52:50 -08:00
Leonardo de Moura
35ad156a46 fix(tests/lean): make sure pretty print and parse test passes
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2014-01-24 17:23:55 -08:00
Leonardo de Moura
8f455f5965 fix(frontends/lean): bug in scope construct
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2014-01-24 17:23:29 -08:00
Leonardo de Moura
7f3e2b3ef4 fix(frontends/lean/parser): bug in 'using' construct
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2014-01-24 17:09:46 -08:00
Leonardo de Moura
8e0888828d fix(library/simplifier): missing check in mk_hcongr_th
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2014-01-24 17:09:46 -08:00
Leonardo de Moura
1a3660180e test(tests/lean): add new simplifier test
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2014-01-24 17:09:46 -08:00
Leonardo de Moura
26bea77721 fix(library/simplifier): bug in heterogeneous equality support, and universe commutativity support in the simplifier
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2014-01-24 17:09:46 -08:00
Leonardo de Moura
009217b499 feat(builtin/hep): replace hallext axiom with theorem
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2014-01-24 17:09:20 -08:00
Leonardo de Moura
dbc100cc2e feat(library/simplifier): cast elimination in the simplifier
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2014-01-23 17:28:14 -08:00
Leonardo de Moura
cd87cb3de4 test(tests/lean): add test for congruence theorem that uses an argument before simplification
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2014-01-23 13:26:09 -08:00
Leonardo de Moura
180be5c4a2 feat(library/simplifier): improve contextual simplifications
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2014-01-23 13:11:58 -08:00
Leonardo de Moura
5ba2525eab test(tests/lean): add test disabling contextual simplifications
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2014-01-23 12:57:05 -08:00
Leonardo de Moura
33193e1ab3 feat(library/simplifier): improve contextual simplifications
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2014-01-23 12:54:29 -08:00
Leonardo de Moura
d6692264e8 feat(library/simplifier): contextual simplifications
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2014-01-23 12:23:22 -08:00
Leonardo de Moura
1638a7bb02 fix(frontends/lean/pp): compute local shared nodes, and avoid unnecessary let's
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2014-01-22 21:44:24 -08:00
Leonardo de Moura
17cce340f6 fix(library/elaborator): in optimization for metavariable free terms
The optimization was incorrect if the term indirectly contained a metavariable.
It could happen if the term contained a free variable that was assigned in the context to a term containing a metavariable.

This commit also adds a new test that exposes the problem.

Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2014-01-22 18:06:00 -08:00
Leonardo de Moura
8214c7add4 feat(library/elaborator): compensate the lack of eta-reduction (and eta-expanded normal forms) in the kernel normalizer
Before this commit, the elaborator was solving constraints of the form

       ctx |- (?m x) == (f x)
as
       ?m <- (fun x : A, f x)    where A is the domain of f.

In our kernel, the terms f and (fun x, f x) are not definitionally equal.
So, the solution above is not the only one. Another possible solution is

       ?m  <- f

Depending of the circumstances we want  ?m <- (fun x : A, f x) OR ?m <- f.
For example, when Lean is elaborating the eta-theorem in kernel.lean, the first solution should be used:
       ?m <- (fun x : A, f x)

When we are elaborating the axiom_of_choice theorem, we need to use the second one:
       ?m <- f

Of course, we can always provide the parameters explicitly and bypass the elaborator.
However, this goes against the idea that the elaborator can do mechanical steps for us.

This commit addresses this issue by creating a case-split
       ?m <- (fun x : A, f x)
       OR
       ?m <- f

Another solution is to implement eta-expanded normal forms in the Kernel.

With this change, we were able to cleanup the following "hacks" in kernel.lean:
     @eps_ax A (nonempty_ex_intro H) P w Hw
     @axiom_of_choice A B P H
where we had to explicitly provided the implicit arguments

This commit also improves the imitation step for Pi-terms that are actually arrows.

Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2014-01-22 13:28:54 -08:00
Leonardo de Moura
6cb4d165c9 feat(builtin/kernel): dependent version of axiom of choice
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2014-01-22 11:04:27 -08:00
Leonardo de Moura
88b6778a1f fix(emacs): syntax highlight
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2014-01-22 09:44:12 -08:00
Leonardo de Moura
66553268d0 feat(builtin/kernel): add skolem_th, we need it to justify skolemization preprocessing step
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2014-01-22 09:41:07 -08:00
Leonardo de Moura
d9b5ebc738 refactor(builtin/kernel): cleanup Hilbert operator definition
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2014-01-22 09:18:40 -08:00
Leonardo de Moura
bcf60db23b fix(builtin/kernel): Hilbert operator only for non-empty types
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2014-01-22 08:52:31 -08:00
Leonardo de Moura
94a3136904 feat(builtin/kernel): add Hilbert's operator, and derive axiom of choice using it
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2014-01-22 08:21:11 -08:00
Leonardo de Moura
425d31f513 chore(library/simplifier): fix style warning
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2014-01-21 21:45:55 -08:00
Leonardo de Moura
cca15f1390 feat(library/simplifier): congruence theorem compilation
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2014-01-21 21:16:23 -08:00
Leonardo de Moura
029d74ec11 chore(kernel): remove comment, we decided to have Eta as a simplification rule
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2014-01-21 14:35:05 -08:00
Leonardo de Moura
95b6e61738 feat(kernel/max_sharing): check for imminent stack overflows and interruptions in the expression sharing maximizer
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2014-01-21 14:33:49 -08:00
Leonardo de Moura
2089b85532 refactor(kernel/instantiate): remove code duplication
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2014-01-21 14:30:38 -08:00
Leonardo de Moura
7299b2d5d6 chore(kernel): remove dead file
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2014-01-21 14:21:13 -08:00
Leonardo de Moura
fbaf6e887f refactor(builtin/kernel): put the congruence theorems in a format that is easier for the simplifier to process
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2014-01-21 14:03:51 -08:00
Leonardo de Moura
331b5846c6 test(library/simplifier): add test for the single_pass option in the simplifier
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2014-01-21 13:47:54 -08:00
Leonardo de Moura
ead54bbf57 feat(library/simplifier): enforce max_steps option
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2014-01-21 12:12:17 -08:00
Leonardo de Moura
1ccfac5873 feat(library/simplifier): conditional rewriting
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2014-01-20 21:15:46 -08:00
Leonardo de Moura
1ef75a9ba6 test(tests/lua): add test/example that demonstrates how to collect statistics of used theorems
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2014-01-20 18:04:22 -08:00
Leonardo de Moura
6bcd8e3ee5 fix(library/expr_lt): use expression depth instead of size to obtain a monotonic total order on terms
It is not incorrect to use size, but it can easily overflow due to sharing.
The following script demonstrates the problem:

local f = Const("f")
local a = Const("a")
function mk_shared(d)
   if d == 0 then
      return a
   else
      local c = mk_shared(d-1)
      return f(c, c)
   end
end
print(mk_shared(33):size())

Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2014-01-20 17:40:49 -08:00
Leonardo de Moura
cd19d4da01 feat(library/simplifier): memoize intermediate results
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2014-01-20 17:03:44 -08:00
Leonardo de Moura
97ead50a3e feat(builtin/Nat): flip orientation of associativity axioms for + and *
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2014-01-20 15:38:00 -08:00